Transient hydromagnetic couple‐stress flow over an infinite vertical cylinder: A unified numerical exploration of thermal radiation and Arrhenius activation energy kinetics

Abstract

Couple‐stress fluids characterize the rheological behaviour of microstructure suspensions such as polymeric melts, lubricants, biological fluids, and colloidal mixtures. These fluids exhibit particle‐scale rotations and size‐dependent characteristics that significantly affect the transfer of momentum and energy. Such behaviours become especially pronounced near curved or cylindrical surfaces, which are central to industrial processes like coating, extrusion, geothermal drilling, and heat exchange systems. Under high‐temperature or chemically reactive conditions, radiative heat transfer emerges as a major mode of energy transport, while the Arrhenius‐type activation energy dictates the rate of species conversion in catalytic reactors, polymerization mechanisms, and reactive fluid flows. This interplay calls for a unified analysis that considers both radiative and activation‐controlled effects. The present study investigates the unsteady transport phenomena of a non‐Newtonian fluid past an infinitely long vertical cylinder, incorporating the combined effects of thermal radiation and Arrhenius activation energy. The nonlinear governing equations for the flow field, thermal profile, and species distribution are discretized in the radial direction using second‐order central finite differencing and integrated over time via the method of lines to ensure numerical stability and accuracy. Computational outcomes reveal that the couple‐stress parameter () accelerates the velocity distribution, thermal profile, and species distribution. Increasing the magnetic parameter () and decreasing the Darcy parameter () reduces velocity but increases temperature and concentration. The radiation parameter significantly enhances fluid temperature, whereas increasing the activation parameter promotes species accumulation. Comparisons with earlier works confirm the validity of the present formulation, and the generated insights are pertinent to thermal and industrial applications such as polymer extrusion, catalytic processing, electronic cooling, and biophysical fluid transport, where microstructural and thermo‐chemical interactions play a decisive role.